Nonabelions in the fractional quantum Hall effect

Moore, Gregory W.; Read, N.

doi:10.1016/0550-3213(91)90407-O

Nonabelions in the fractional quantum Hall effect

Gregory W. Moore
(
- Yale U.
)
,
N. Read
(
- Yale U.
)

1991

35 pages

Published in:

Nucl.Phys.B 360 (1991) 362-396

Published: 1991

DOI:

10.1016/0550-3213(91)90407-O

View in:

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Abstract:

Applications of conformal field theory to the theory of fractional quantum Hall systems are discussed. In particular, Laughlin's wave function and its cousins are interpreted as conformal blocks in certain rational conformal field theories. Using this point of view a hamiltonian is constructed for electrons for which the ground state is known exactly and whose quasihole excitations have nonabelian statistics; we term these objects “nonabelions”. It is argued that universality classes of fractional quantum Hall systems can be characterized by the quantum numbers and statistics of their excitations. The relation between the order parameter in the fractional quantum Hall effect and the chiral algebra in rational conformal field theory is stressed, and new order parameters for several states are given.

Hall effect: fractional
field theory: conformal
field theory: rational
wave function
algebra: chiral
statistics: nonabelian
Wess-Zumino-Witten model
bibliography

References(59)

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[1]

Classical and Quantum Conformal Field Theory

- Commun.Math.Phys. 123 (1989) 177
•
DOI:
- 10.1007/BF01238857

[2]

LecturesBanff Summer School

J. Fröhlich

[3]

The quantum Hall effect

S. Girvin
,
R. Prange

[4]

Order parameter and Ginzburg-Landau theory for the fractional quantum Hall effect

N. Read
(
- MIT
)

- Phys.Rev.Lett. 62 (1989) 86-89
•
DOI:
- 10.1103/PhysRevLett.62.86

[5]

Quantum Field Theory and the Jones Polynomial

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Commun.Math.Phys. 121 (1989) 351-399,
•
DOI:
- 10.1007/BF01217730

[6]

G. Moore
,
N. Seiberg

- Phys.Lett. 220 (1989) 422

[7]

Statistics of quasiparticles and the hierarchy of fractional quantized Hall states

B.I. Halperin
(
- Harvard U.
)

- Phys.Rev.Lett. 52 (1984) 1583-1586,
- Phys.Rev.Lett. 52 (1984) 2390 (erratum)
•
DOI:
- 10.1103/PhysRevLett.52.1583

[8]

Fractional Statistics and the Quantum Hall Effect

D. Arovas
(
- UC, Santa Barbara
)
,
J.R. Schrieffer
(
- UC, Santa Barbara
)
,
Frank Wilczek
(
- UC, Santa Barbara
)

- Phys.Rev.Lett. 53 (1984) 722-723,
- In *Stone, M. (ed.): Quantum Hall effect* 145-146. In *Wilczek, F. (ed.): Fractional statistics and anyon superconductivity* 256-257
•
DOI:
- 10.1103/PhysRevLett.53.722

[9]

The quantum Hall effect

S.M. Girvin

[9]

Off diagonal long range order, oblique confinement, and the fractional quantum Hall effect

S.M. Girvin
(
- NIST, Wash., D.C.
)
,
A.H. MacDonald
(
- CRPP, Ottawa
)

- Phys.Rev.Lett. 58 (1987) 1252-1255,
- Reprinted in *Wilczek, F. (ed.): Fractional statistics and anyon superconductivity* 258-261
•
DOI:
- 10.1103/PhysRevLett.58.1252

[10]

An effective field theory model for the fractional quantum hall effect

- Phys.Rev.Lett. 62 (1988) 82-85
•
DOI:
- 10.1103/PhysRevLett.62.82

[11]

Nonabelian Bosonization in Two-Dimensions

Edward Witten
(
- Princeton U.
)

- Commun.Math.Phys. 92 (1984) 455-472,
•
DOI:
- 10.1007/BF01215276

[12]

unpublished

T. Banks
,
I. Klebanov
,
J. Lykken
,
L. Susskind

[13]

Santa Barbara preprints

X.G. Wen

[*]

Santa Barbara preprint

X.G. Wen
,
Q. Niu

[14]

Phys.Rev.Lett.

R. Willett

[15]

J.P. Eisenstein

- Phys.Rev.Lett. 61 (1988) 997

[16]

Holonomy, the quantum adiabatic theorem, and Berry's phase

Barry Simon
(
- Caltech
)

- Phys.Rev.Lett. 51 (1983) 2167-2170
•
DOI:
- 10.1103/PhysRevLett.51.2167

[17]

Appearance of Gauge Structure in Simple Dynamical Systems

Frank Wilczek
(
- Santa Barbara, KITP
)
,
A. Zee
(
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 52 (1984) 2111-2114,
- IN *SHAPERE, A. (ED.), WILCZEK, F. (ED.): GEOMETRIC PHASES IN PHYSICS* 141-144. (PHYS. REV. LETT. 52 (1984) 2111-2114) AND CALIF. UNIV. SANTA BARBARA - NSF-ITP-84-051 (84,REC.MAY) 13 P. (SEE BOOK INDEX)
•
DOI:
- 10.1103/PhysRevLett.52.2111